Form Factors of BranchPoint Twist Fields in Quantum Integrable Models and Entanglement Entropy
Abstract
In this paper we compute the leading correction to the bipartite entanglement entropy at large subsystem size, in integrable quantum field theories with diagonal scattering matrices. We find a remarkably universal result, depending only on the particle spectrum of the theory and not on the details of the scattering matrix. We employ the "replica trick" whereby the entropy is obtained as the derivative with respect to n of the trace of the nth power of the reduced density matrix of the subsystem, evaluated at n=1. The main novelty of our work is the introduction of a particular type of twist fields in quantum field theory that are naturally related to branch points in an nsheeted Riemann surface. Their twopoint function directly gives the scaling limit of the trace of the nth power of the reduced density matrix. Taking advantage of integrability, we use the expansion of this twopoint function in terms of form factors of the twist fields, in order to evaluate it at large distances in the twoparticle approximation. Although this is a wellknown technique, the new geometry of the problem implies a modification of the form factor equations satisfied by standard local fields of integrable quantum field theory. We derive the new form factor equations and provide solutions, which we specialize both to the Ising and sinhGordon models.
 Publication:

Journal of Statistical Physics
 Pub Date:
 January 2008
 DOI:
 10.1007/s109550079422x
 arXiv:
 arXiv:0706.3384
 Bibcode:
 2008JSP...130..129C
 Keywords:

 Integrable quantum field theory;
 Entanglement entropy;
 Form factors;
 Twist fields;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 40 pages, 10 eps figures